What is the value of ln root(4)(e) ? Answer:

Understand the expression: Understand the expression ln root(4)(e). The expression ln root(4)(e) means the natural logarithm of the fourth root of e, where e is the base of the natural logarithm, approximately equal to 2.71828. The fourth root of a number is the number that, when raised to the power of 4, gives the original number. So, we need to find the fourth root of e and then take the natural logarithm of that value.Calculate the fourth root of e: Calculate the fourth root of e. The fourth root of e can be written as e^(1/4). This is because the nth root of a number can be expressed as that number raised to the power of 1/n.Take the natural logarithm: Take the natural logarithm of the fourth root of e. Since the natural logarithm ln(x) is the inverse function of the exponential function e^x, we have the property that ln(e^x) = x. Applying this property to our expression, we get ln(e^(1/4)) = 1/4.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the value of
ln root(4)(e) ?
Answer:

What is the value of $\ln \sqrt[4]{e}$ ?

View step-by-step help

Full solution

Q. What is the value of

\ln \sqrt[4]{e}

Understand the expression: Understand the expression $\ln \sqrt[4]{e}$ . The expression $\ln \sqrt[4]{e}$ means the natural logarithm of the fourth root of $e$ , where $e$ is the base of the natural logarithm, approximately equal to $2.71828$ . The fourth root of a number is the number that, when raised to the power of $4$ , gives the original number. So, we need to find the fourth root of $e$ and then take the natural logarithm of that value.
Calculate the fourth root of $e$ : Calculate the fourth root of $e$ . The fourth root of $e$ can be written as $e^{(1/4)}$ . This is because the $n$ th root of a number can be expressed as that number raised to the power of $1/n$ .
Take the natural logarithm: Take the natural logarithm of the fourth root of $e$ . Since the natural logarithm $\ln(x)$ is the inverse function of the exponential function $e^x$ , we have the property that $\ln(e^x) = x$ . Applying this property to our expression, we get $\ln(e^{1/4}) = \frac{1}{4}$ .